During seismic data acquisition, seismic sources generate seismic waves that propagate into the earth. Once underground, a seismic wave can reflect upward when it interacts with a reflector, which causes the seismic wave to return to the free surface where the signal can be detected by a seismic receiver. Seismic data collected at the surface is usually a composite signal that includes signals from primary reflection events as well as multiple reflection events. As used herein, the term “multiple” and its related terms refer to a reflection event in which a propagating seismic wave undergoes at least one downward reflection before reflecting upward to reach a seismic receiver. More particularly, an internal multiple is characterized by at least one downward reflection from a boundary or interface below the free surface with no downward reflection from the free surface. Internal multiples are created by changes in density or velocity of subterranean structure between the surface (earth surface or sea floor) and a target reflector (such as a hydrocarbon layer, fresh water aquifer, and so forth).
Multiples are generally undesirable for seismic imaging and techniques have been developed for attenuating multiples during pre-migration processing. Inverse scattering series is an established multiple attenuation technique that is attractive because of its purely data driven (sub-surface information is not required) approach. Inverse scattering series is powerful because it can be used to predict all internal multiples simultaneously in one run. However, a major drawback is that the computational cost of conventional inverse scattering series is significantly higher than other pre-stack processing and imaging flows. Currently, the computing cost for inverse scattering series is generally considered prohibitive for 3D seismic imaging applications involving real data.